Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
472 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#4072 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. #11716611 | C2 | semidirect |
| 9. #87900 | C4 | semidirect |
| 11. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 13. C2×#6045 | C4 | semidirect |
| 16. C4×C5×Dic5 | C22 | semidirect |
| 18. C5×#681 | C22 | semidirect |
| 46. #4072 | D5 | semidirect |
| 47. C2×#681 | D5 | semidirect |
| 97. C4×Dic5 | C2×D5 | semidirect |
| 99. #681 | C2×D5 | semidirect |
| 166. C52 | #421 | semidirect |
| 252. C5 | #65294 | semidirect |
| 253. C5 | #65428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C5×#4072 | 2 |
| C2×C5×#681 | 2 |
| #11716611 | 2 |
| #65428 | 5 |
| #65294 | 5 |